"Some people, however, seem to feel a desperate need to be accepted as a 'woman' or an a 'man.' "

They have a compulsive disorder. That needs to be respected: if "identifying" as another gender alleviates their desperation, then we should support that.

It is a tiny fraction of the population though, and we should not conflate that disorder with young people reflecting "I should have been born a woman", etc. It is not the same thing. Just because you think that you are "like a woman inside" does not make you a woman, etc. There is no need to embrace a label for how you feel in your mind.